SPG:Running

Notes:

Research applies to all four of the Sega Mega Drive games, and Sonic CD.

The following describes ground speed, the forces that impact it and the effects of player input. It only applies when Sonic is on dry land with no special power-ups. Curves, water physics, Super Sonic, and Speed Shoes will be covered in separate guides.

Variables

The following variables/constants will be referenced frequently in this section.

//Variables
xsp: the speed in which sonic is moving horizontally
ysp: the speed in which sonic is moving vertically
gsp: the speed in which sonic is moving on the ground	
//Constants
acc: 0.046875
dec: 0.5
frc: 0.046875 (same as acc)
top: 6

Ground Speed Conversion

gsp is used to calculate xsp and ysp when on the ground. This is further described in The Three Speed Variables.

xsp = gsp*cos(angle);
ysp = gsp*-sin(angle);

Movement

Note: In the original games, holding and at the same time will run both direction's code in one step, if you want in your engine, you can disable + input (Emulators like Fusion will just cancel the right input if left is also held).

Acceleration

If you're holding , Sonic's gsp decreases by acc every step. If you're holding (Also applies if you're holding , which you may not want in your engine), his gsp increases by acc every step.

Deceleration

If Sonic is already moving when you press or , rather than at a standstill, it's checked whether you are holding the direction he's already moving. If so, acc is added to his gsp as normal. However if you are pressing in the opposite direction than he's already moving, the deceleration constant (dec) is added instead. Thus Sonic can turn around quickly. If no distinction is made between acc and dec, Sonic takes too long to overcome his current velocity, frustrating the player. A good engine must not make such a day one mistake.

One might think that if gsp happened to equal 0.1, and you pressed , dec would be subtracted, resulting in an gsp value of -0.4. Oddly, this is not the case in any of the original games. Instead, at any time an addition or subtraction of dec results in gsp changing sign, gsp is set to 0.5 in the opposite direction. For example, in the instance above, gsp would become -0.5. The bizarre result of this is that you can press for one step, and then press (or vice versa), and start running faster than if you had just pressed alone! Now, the resulting speed is still lower than one pixel per step, so it isn't very noticeable, but nonetheless it is true.

Friction

If you are not pressing or , friction (frc) kicks in. In any step in which the game recieves no horizontal input, frc is subtracted from gsp (depending on the sign of gsp), where if it then passes over 0, it's set back to 0.

Top Speed

Sonic can only accelerate up to a certain point. At some point, he reaches top speed and can no longer move any faster under his own power. So, after acc is added to gsp, if gsp exceeds top it's set to top.

In Sonic 1, while Sonic is already running at a higher speed than he can possibly achieve on his own (such as having been impelled by a spring), if you press in the direction he's moving, acc will be added to gsp as usual. However, notice that gsp now exceeds top, which means gsp will be set to top. Thus it is possible to curtail your forward momentum by pressing in the very direction of your motion. This can be solved in your engine (and was fixed in Sonic 2 and beyond) by checking to see if gsp is less than top before adding acc. Only if gsp is already less than top will it check if gsp exceeds top.

Sonic CD and Sonic 2 actually has a fix like this, where the top check won't happen if gsp is already above top, because in Sonic CD can perform the "Super Peel Out", which launches him above his typical top, and in Sonic 2 because it's supposed to be a much faster game. The issue is, in both games, it doesn't fix this error when Sonic is in mid-air, causing him to usually lose his speed when running off of a ledge.

Here's some code logic that can accurately emulate movement and friction:

if (the player is pressing left)
{
    if (gsp > 0)
    {
        gsp -= dec;
        if (gsp <= 0)
            gsp = -0.5;
    }
    else if (gsp > -top)
    {
        gsp -= acc;
        if (gsp <= -top)
            gsp = -top;
    }
}

if (the player is pressing right)
{
    if (gsp < 0)
    {
        gsp += dec;
        if (gsp >= 0)
            gsp = 0.5;
    }
    else if (gsp < top)
    {
        gsp += acc;
        if (gsp >= top)
            gsp = top;
    }
}

if (the player is not pressing left or right)
    gsp -= minimum(absolute(gsp), frc) * sign(gsp);